M.Jansen Utter tosh.
What alfaman said is correct.
The TCAS on the aircraft cares not one iota about flight direction; it will compute the best avoidance action based on projected flight paths.
When a controller becomes aware there is about to be a loss of separation (prior to TCAS becoming involved), the controller will take whatever steps required to put it right, and direction of flight according to the quadrantal level rules will have little to do with it.